This explains why the clock on the destination planet reads 20 years from the ship-based observer, even though he knows the clock must have only been ticking for 15 years since the ship left Earth. It's because from the ship's reference frame, the two clocks were not started at the same time and the clock on the destination planet has been started 5 years before the ship's clock was started. This part can be calculated using a Lorentz transformation to compare the space-time coordinates of an event in different inertial reference frames.
Confusing stuff... But you are saying that the guy left on the planet will read 15 years on the same clock?
What happens when you land your spaceship?
Will the decelleration make the clocks "synchronize", otherwise guy A on planet and B on the ship will have a big problem deciding on a time to meet eachother...
If you never land, but have some kind of way to communicate, would guy A and B start to argue about what time the clock is showing?
Or would communication be impossible?
The observer on the planet will read 15 years on the ship's clock, when the ship arrives, yes. This is the same time that the ship-based observer read on the ship's clock. The ship-based observer reads 20 years on the planet's clock and the planet-based observer reads 20 years on the planet's clock. The two observers are in complete agreement.
Whether you land the spaceship or not doesn't matter! Nothing would change at all. There is no synchronization involved and there is no contradiction either.
Time has indeed been shorter for the observer travelling on a spaceship, there is asymmetry in this situation (because the spaceship undergoes changes of velocity but the planet does not).
Keep in mind that when the spaceship has just been launched from Earth, then the reference frame of the Earth and the reference frame of the spaceship disagree about when the clock on the destination planet was started relative to when the ship-based clock was started. But that's because the ship-based clock and the destination planet's clock are physically separated. When the ship arrives at its destination, then because the two clocks are at the same location, it doesn't matter at all which frame of reference you choose, they will all be in agreement about the two clocks.